Question

it has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field a random sample of 420 incoming college freshmen were asked their preference and 84 replied that they were considering business as a major estimate the true proportion of freshmen business majors with 94% confidence round intermediate calculations to three decimal places round final answer to one

Answer 1

SOLUTION:

From given data,

it has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field a random sample of 420 incoming college freshmen were asked their preference and 84 replied that they were considering business as a major estimate the true proportion of freshmen business majors with 94% confidence

We are given that 20.4% of incoming freshmen indicate that they will major in business or a related field .

so, P = 20.4 / 100 = 0.204

A random sample of size 420 is taken

so n= 420

in the sample 84 replied that they are belong to business so the true proportion

= 84 / 420 = 0.2

= 1-

= 1- 0.2

= 0.8

The 94% confidence interval  

94/100 = 0.94

= 1- 0.94 = 0.06

Z_/2   = Z _0.06/2 = Z _0.03 = 1.88

0.2   1.88

0.2 1.88 ( 0.019518 )

0.2   0.03669384

(0.2 - 0.03669384 ) ,(0.2+ 0.03669384 )

(0.16330616 , 0.23669384)

Hence we can say that 94% confidence that the true percentage is between 16.330%. and 23.669%